We propose a lensfree on-chip microscopy approach for wide-field quantitative phase imaging (QPI) based on wavelength scanning. Unlike previous methods, we found that a relatively large-range wavelength diversity not only provides information to overcome spatial aliasing of the image sensor but also creates sufficient diffraction variations that can be used to achieve motion-free, pixel-super-resolved phase recovery. Based on an iterative phase retrieval and pixel-super-resolution technique, the proposed wavelength-scanning approach uses only eight undersampled holograms to achieve a half-pitch lateral resolution of 691 nm across a large field-of-view of 29.85mm2, surpassing 2.41 times the theoretical Nyquist-Shannon sampling resolution limit imposed by the pixel size of the sensor (1.67 µm). We confirmed the effectiveness of this technique in QPI and resolution enhancement by measuring the benchmark quantitative phase microscopy target. We also showed that this method can track HeLa cell growth within an incubator, revealing cellular morphologies and subcellular dynamics of a large cell population over an extended period of time.